
Chair: Reinhold Schneider

09:00  10:00

Jiří Pittner
(Czech Academy of Sciences)
Recent progress in the DMRGtailored CC approach
We present the relativistic version of the DMRGtailored coupled cluster
method (DMRGTCC), aimed at calculations of strongly correlated systems containing heavy atoms.
The method allows to include dynamical correlation at lower computational costs with respect to DMRG in a very large active space, as we demonstrate on the system of TlH.
We also present a (nonrelativistic) implementation of DMRGTCCSD and
TCCSD(T) based on the domainbased local pair natural orbital approach
(DLPNO) in Orca, which is able to treat large molecules, for example
oxoMn(Salen) or Iron(II)porphyrin complex.

10:00  10:15

Break

10:15  10:45

HongHao Tu
(Technische Universität Dresden)
Density matrix renormalization group boosted by Gutzwiller projected wave functions
The density matrix renormalization group (DMRG), with matrix product states (MPSs) being the underlying variational ansatz, is one of the most powerful numerical methods for studying quantum manybody systems. The Gutzwiller projected wave functions provide another important family of variational ansatz in condensed matter and quantum chemistry. I will discuss our recent progress on devising methods to convert Gutzwiller projected wave functions into MPSs and using them to initialize DMRG simulations. I will show that the performance of DMRG can be drastically improved by initializing with a properly chosen Gutzwiller ansatz. This also allows to quantify the closeness of the initial Gutzwiller ansatz and the final converged state after DMRG sweeps, thereby sheds light on whether the Gutzwiller ansatz captures the essential entanglement features of the actual ground state for a given Hamiltonian.

10:45  11:00

Break

11:00  12:00

George Booth
(King's College London)
From entanglement to the matrix product state: Tensor network tools reimagined for new methods
The success of DMRG as a method in recent years can be considered to be built on two pillars of understanding. These come from the ideas of renormalization and entanglement, and from the form of the matrix product state as a wave function ansatz. We take these two concepts, and motivated by their use in tensor networks, take them in a different direction to develop new methods with potential in electronic structure.
In the first part, we will show how the idea of Schmidt decomposition approaches can be extended to the idea of generating 1body or 2body 'bath' states, rather than the nbody entanglement used in tensor networks. We will use these to develop the idea of a local embedding in the quantum chemistry of real materials, as well as renormalized spectral approaches via a combination with diagrammatic techniques.
In the second part, we will examine the form of the MPS ansatz, and ask whether modifications to its form can extend the model naturally to higher dimensions in a tractable way. From this, we will introduce the 'Quantum Gaussian Process State'  a new wave function ansatz, originally developed from machine learning principles, but equallywell motivated from a tensor network perspective.
Refs:
Fully Algebraic and Selfconsistent Effective Dynamics in a Static Quantum Embedding, PV Sriluckshmy, M Nusspickel, E Fertitta, GH Booth
arXiv:2012.05837 (2021)
A wave function perspective and efficient truncation of renormalised secondorder perturbation theory, OJ Backhouse, M Nusspickel, GH Booth,
J. Chem. Theory Comput. 16, 1090 (2020)
Efficient excitations and spectra within a perturbative renormalization approach, OJ Backhouse, GH Booth
J. Chem. Theory Comput. 16, 10, 6294–6304 (2020)
Gaussian Process States: A datadriven representation of quantum manybody physics, A Glielmo, Y Rath, G Csanyi, A De Vita, GH Booth
Phys. Rev. X 10, 041026 (2020)

12:00  12:15

Break

12:15  12:45

Alberto Baiardi
(ETH Zurich)
Quantum Dynamics with the TimeDependent Density Matrix Renormalization Group
Thanks to the advent of ultrafast spectroscopic techniques, the dynamics of a molecule can be resolved experimentally on the natural time scales of both its electronic and nuclear motions. In principle, the exact quantum dynamics of a molecular system [1,2] in a given basis can be simulated with Full Configuration Interaction (fullCI) methods. The exponential increase of the computational cost of fullCI hinders, however, straightforward applications to large molecular systems. In this contribution, we show how to limit this unfavorable scaling by expressing the wave function as a matrix product state, a parameterization employed in the Density Matrix Renormalization Group algorithm (DMRG) [3]. The different strategies that have been designed to integrate the resulting equation of motion are broadly defined as timedependent DMRG (TDDMRG).
We generalize a recently developed tangent spacebased TDDMRG algorithm [4] to electronic [5] and vibrational [6] quantum chemical Hamiltonians. We apply the resulting theory to simulate the nuclear and electronic dynamics, possibly coupled together, of molecules with several dozens of degrees of freedom. We assess the accuracy of the simulations by comparison with stateoftheart CI results.
We also generalize TDDMRG to imaginarytime and show that the resulting method can optimize the groundstate wave function of nonHermitian Hamiltonians. We apply this imaginarytime TDDMRG variant to the similarity transformed transcorrelated Hamiltonian [7] and demonstrate that the resulting method, transcorrelated DMRG (DMRG) [8], can enhance the DMRG convergence for molecular calculations.
References:
[1] Meyer H. D., WIRES Comp. Mol Sci. 2011, 2, 351.
[2] Sato T., Ishikawa K. L., Phys. Rev. A. 2013, 88, 023402.
[3] Baiardi A., Reiher M., J. Chem. Phys., 2020, 152, 040903.
[4] Haegeman J., Lubich C., Oseledets I., Vandereycken F., Phys. Rev. B. 2016, 94, 1.
[5] Baiardi A., Reiher M., J. Chem. Theory Comput. 2019, 15, 3481.
[6] Baiardi A., Arxiv 2020, 2010.02049.
[7] Boys S. F., Handy N. C., Proc. Roy. Soc. A. 1969, 310, 1500.
[8] Baiardi A., Reiher M., J. Chem. Phys. 2020, 153, 164115.

12:45  17:00

Informal discussions


Chair: Dirk Andrae

17:00  18:00

Karen Hallberg
(Instituto Balseiro and Centro Atomico Bariloche, CNEA and CONICET)
Precision spectral densities in correlated systems
We present an efficient numerical method to calculate spectral densities of complex impurities based on the Density Matrix Renormalization Group (DMRG) and use it as the impurity solver of the Dynamical Mean Field Theory (DMFT). By using a selfconsistent bath configuration with very low entanglement, we take full advantage of the DMRG to calculate dynamical response functions paving the way to treat large effective impurities such as those corresponding to multiorbital interacting models and multisite or multimomenta clusters. It also solves for complex impurities using abinitio input which opens its realm of applications to real materials. This method leads to reliable calculations of nonlocal self energies on the real frequency axis directly, at zero temperature, arbitrary dopings and interactions and at all energy scales.
We will show results for multisite and multiorbital models in which interesting features arise such as emergent lowenergy bound states.

18:00  18:15

Break

18:15  19:15

Stefan Knecht
(GSI Darmstadt)
Matrix Product States Approaches for the whole Periodic Table of the Elements
Computational modelling has undoubtedly become an integral part of chemical research. For instance, providing an understanding of the nature of a chemical bond and how it relates to the chemical reactivity of a molecule is of central interest for chemistry. To rationalize such properties at a molecular level requires a tailormade quantum chemical framework
that provides the means to accurately describe the central piece of information relevant to chemistry, viz., the electronic structure. Its determination relies on the solution of the quantum mechanical equations for the electronic manybody problem. Whereas solving the electronic Schrödinger equation (often) yields sufficiently accurate results for light elements, i.e., those of the upper part of the periodic table, this is generally not the case for heavy elements. For the latter, an explicit consideration of the theory of special relativity is required.
In this talk, the development and application of matrixproductstate based multiconfigurational quantum chemical methods [17]
is presented that are designed to accommodate the needs to account for the correlated motion of the electrons as well as for relativistic effects in a rigorous manner.
[1] S. Knecht, Ö. Legeza, M. Reiher, J. Chem. Phys.,140, 041101 (2014).
[2] S. Knecht, S. Keller, J. Autschbach, M. Reiher, J. Chem. Theory Comput., 12, 5881 (2016).
[3] S. Battaglia, S. Keller, S. Knecht, J. Chem. Theory Comput., 14, 2353 (2018).
[4] S. Knecht, H. J. Aa. Jensen, T. Saue, Nat. Chem.,11, 40 (2019).
[5] S. Knecht, Nachr. Chem., 67, 57 (2019).
[6] S. Knecht, in preparation, 2020.
[7] J. Paquier, S. Knecht, J. Toulouse, work in progress, 2020.

19:15  19:30

Break

19:30  20:00

Norbert Schuch
(University of Vienna)
Matrix product state algorithms for Gaussian fermionic states
While general quantum manybody systems require exponential resources to be simulated on a classical computer, systems of noninteracting fermions can be simulated exactly using polynomially scaling resources. Such systems may be of interest in their own right, but also occur as effective models in numerical methods for interacting systems, such as HartreeFock, density functional theory, and many others. Often it is desirable to solve systems of many thousand constituent particles, rendering these simulations computationally costly despite their polynomial scaling. We demonstrate how this scaling can be improved by adapting methods based on matrix product states, which have been enormously successful for lowdimensional interacting quantum systems, to the case of free fermions. Compared to the case of interacting systems, our methods achieve an exponential speedup in the entanglement entropy of the state. We demonstrate their use to solve systems of up to one million sites with an effective MPS bond dimension of 10^15.

20:00  20:15

Closing remarks
